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Quantum annealers have been designed to propose near-optimal solutions toNP-hard optimization problems. However, the accuracy of current annealers suchas the ones of D-Wave Systems, Inc., is limited by environmental noise andhardware biases. One way to deal with these imperfections and to improve thequality of the annealing results is to apply a variety of pre-processingtechniques such as spin reversal (SR), anneal offsets (AO), or chain weights(CW). Maximizing the effectiveness of these techniques involves performingoptimizations over a large number of parameters, which would be too costly ifneeded to be done for each new problem instance. In this work, we show that theaforementioned parameter optimization can be done for an entire class ofproblems, given each instance uses a previously chosen fixed embedding.Specifically, in the training phase, we fix an embedding E of a complete graphonto the hardware of the annealer, and then run an optimization algorithm totune the following set of parameter values: the set of bits to be flipped forSR, the specific qubit offsets for AO, and the distribution of chain weights,optimized over a set of training graphs randomly chosen from that class, wherethe graphs are embedded onto the hardware using E. In the testing phase, weestimate how well the parameters computed during the training phase work on arandom selection of other graphs from that class. We investigate graphinstances of varying densities for the Maximum Clique, Maximum Cut, and GraphPartitioning problems. Our results indicate that, compared to their defaultbehavior, substantial improvements of the annealing results can be achieved byusing the optimized parameters for SR, AO, and CW.

Optimizing embedding-related quantum annealing parameters for reducing hardware bias